Preheat the water bath to 156°F (68.9°C).
If the pork shoulder is too large to fit into a bag, cut it into multiple pieces. Mix the spices together in a small bowl then coat the pork with them. Place the pork in a sous vide bag then seal. Place the bag in the water bath and cook the pork for 18 to 24 hours.
Heat some oil in a pot over medium heat.
Add the onion, carrot, peppers, jalapeño and garlic to the oil and cook until softened.
Add the tomatoes, chicken stock, and cornmeal. Bring to a simmer and let barely simmer uncovered for at least 20 minutes, and up to 60 minutes, for the vegetables to break down and the soup to reduce and thicken.
Take the sous vide bag out of the water and remove the cooked pork shoulder. Dry it off thoroughly with a paper towel or dishcloth.
Quickly sear the pork for 1 to 2 minutes per side, until just browned, then remove from the heat.
Shred the pork with a fork and tongs then lightly salt it. You can add the pork juices to the tortilla soup for extra porky flavor.
Place a ladle or two of tortilla soup into a bowl. Add a handful of shredded pork. Top with the avocados, tortilla strips, cheddar cheese, and jalapeño slices. Sprinkle with cilantro, add a dollop of sour cream and serve with a lime wedge on the side.